Assessing the Resilience of Specialized Terminals Within Coastal Port Transportation Systems: An Improved RBOP Method

Abstract

Specialized terminals in coastal ports play an increasingly important role in maritime transport. To enhance the resilience of specialized terminals, it is vital to increase their ability to maintain a certain level of function under various emergencies. This effort is fundamental to ensuring the handling efficiency of coastal ports and the stability of the shipping network. In this paper, from the perspective of the coastal port transportation system, we developed a resilience evaluation framework considering micro-level, meso-level, and macro-level influencing factors on specialized terminals. To evaluate the comprehensive resilience of the specialized terminal, we quantitatively calculated each evaluation indicator and proposed an improved Ranking Based on Optimal Points (RBOP) method. The application results were obtained from a study on specialized container terminals at eight hub ports in coastal China. The improved RBOP method takes into account both the current status and future development trends of specialized terminals. As a result, compared with TOPSIS, VIKOR, Multi-MOORA, and WASPAS, the ranking results of the improved RBOP and the latest method (i.e., WASPAS) are the closest, which only differ in the seventh and eighth ranking, while the outcomes of the improved RBOP align more closely with expert expectations. The proposed method enables the resilience evaluation of specialized terminals from a holistic perspective of the coastal port transportation system. This helps port managers identify bottlenecks in the resilience of specialized terminals and can enhance the efficiency and stability of port operations.

1. Introduction

Due to low prices, large freight volume, and being environmentally friendly and relatively safe, maritime transport plays an important role in international trade; ships carried over 80% of the volume of global trade [1] and have maintained a continuous growth trend since 2020 (see Figure 1). To adapt to the development of the shipping industry, coastal ports, which are the important nodes and hubs of maritime transport, have built many specialized terminals for major cargo handling such as containers, crude oil, iron ore, and coal over the years. Taking China as an example, by the end of 2021, there have been 430 specialized container berths, 41 specialized crude oil berths, 59 specialized iron ore berths, and 254 specialized coal berths in coastal ports in China, accounting for a large proportion of the total throughput. It can be seen that specialized terminals in coastal ports play an increasingly important role in maritime transport.

Efficient and stable operations are important requirements of specialized terminals. However, due to the complexity of the port operation system, the specialized terminal faces various risks. At the micro-level (i.e., in the specialized terminal), the specialized terminal operation can be interrupted by equipment fault or facility destruction due to the aging of equipment and the facility. At the meso-level (i.e., focusing on the entire port), when other facilities, including the waterway, collecting and distributing system, etc., come across an accident, such as a ship collision or grounding in the waterway, it will lead to the interruption of specialized terminal operations. At the macro-level (i.e., considering the port as the hub of the shipping network), the outbreak of local wars and COVID-19 have led to port congestion and even port closure [1], which also has a serious impact on specialized terminals. In this case, it is necessary to analyze the factors affecting the efficiency and stability of specialized terminals from the overall perspective of the coastal port transportation system considering the micro-level, meso-level, and macro-level, to evaluate the influence of various factors quantitatively.

To do so, in this study, considering the actual development of specialized terminals and referring to the definition of resilience in existing studies [2], the resilience of specialized terminals in coastal ports is defined as the ability of specialized terminals (including facilities, handling equipment, transport machinery, management systems, etc.) to withstand, adapt, and recover under emergencies. A specialized terminal with good resilience should have four aspects of capabilities as follows:

(1)

Robustness: The ability of specialized terminals to maintain a certain level of function in the face of major risk events such as natural disasters.

(2)

Redundancy: The facility (or handling equipment) of specialized terminals should have a certain amount of spare capacity or alternative solutions, such as substituting berths in nearby ports. When the functions of some facilities (or handling equipment) are damaged due to emergencies, the alternative solutions can be replenished in time, preventing the transport system from being completely paralyzed.

(3)

Recoverability: Specialized terminals can recover to a certain level of function in a short time after the emergency.

(4)

Adaptability: Specialized terminals can learn from past accidents and improve their adaptability to various emergencies by improving the management mechanism.

Based on the definition of the resilience of specialized terminals, this study aims to put forward a resilience evaluation method of specialized terminals from the perspective of the coastal ports transportation system. Although some existing studies have considered different influencing factors to build a port resilience evaluation framework, most of them consider ports as nodes of the transportation network to adopt complex network theory [3,4], lacking the comprehensive perspective of the micro–meso–macro level. In addition, the studies on comprehensive resilience assessment using Multi-Criteria Decision-Making (MCDM) methods mostly extract the best scheme from the initial decision matrix itself and lack consideration for the preferences of decision-makers and the future development trend of target ports.

To fill the research gap, in this paper, a specialized terminal resilience evaluation framework was constructed first, which considered factors from the micro-level, meso-level, and macro-level. Secondly, the quantitative calculation method of evaluation indicators is provided. Thirdly, an improved Ranking Based on Optimal Point (RBOP) algorithm is proposed to evaluate the comprehensive resilience of specialized terminals. Finally, the validity and practicability of the method are verified by taking eight container ports in coastal China as examples. This study can provide valuable guidance for port stakeholders to improve the resilience of specialized terminals and the stability of handling operations.

The contribution of this study can be divided into three aspects:

(1)

From a comprehensive perspective of the coastal port transportation system, the factors affecting the resilience of specialized terminals at the micro-level, meso-level, and macro-level are qualitatively analyzed.

(2)

The quantitative calculation indicators of the influencing factors are proposed.

(3)

In view of the characteristics of specialized terminals and the coastal port transportation system, an improved RBOP method is proposed to evaluate the resilience of specialized terminals by fully considering the preferences of port stakeholders and the future development trend of ports.

The rest of this paper is organized as follows: Section 2 reviews the existing literature. Section 3 introduces the resilience evaluation framework and the improved RBOP algorithm. In Section 4, the case study is provided. Section 5 summarizes the study.

2. Literature Review

Existing studies on the resilience of port systems can be divided into two parts. One is to evaluate the resilience of the port system itself, the other treats the port as a node of the transport network and studies the resilience of the port transportation network.

2.1. Port System Resilience Evaluation

In terms of port system resilience assessment, most studies establish a port resilience assessment framework by analyzing the factors that affect the port system resilience. Kim et al. proposed a port resilience measuring framework by conducting exploratory and Confirmatory Factor Analysis using 199 samples collected from port stakeholders in South Korea [5]. Liu et al. built a port resilience index system based on the entropy weight method to measure port resilience in the post-COVID-19 era [6]. Al-Mutairi et al. designed a scenario-based preferences modeling method to measure the system resilience of Mubarak Al-Kabeer Port (MKP) in Kuwait [7]. Justice et al. discussed how US container ports improve resilience through innovation and the emergent outputs of self-organized agents (components) of their port organizations [8]. Gu et al. developed a hybrid framework combining Hierarchical Holographic Modeling (HHM) with a fuzzy cognitive map (FCM) to measure port resilience under COVID-19 [9]. Ayaz et al. evaluated the resilience strategies of ports by grounding chaos theory together with the AHP method [10]. Almutairi et al. integrated the stakeholder mapping method and scenario-based preferences modeling for container port resilience analytics [11]. Kim et al. aimed to find out how port security affects port resilience and port operational performance by using the Confirmatory Factor Analysis and Structural Equation Model [12]. Xu et al. utilized global spatial autocorrelation and local spatial autocorrelation to evaluate the resistance and resilience of global ports [13]. Lin et al. constructed a port resilience evaluation model using the CRITIC-entropy method and the TOPSIS method for the port along the Maritime Silk Road [14]. Wang et al. proposed a circular four-stage method to study port resilience based on the Bayesian network [15]. Hossain et al. identified the basic factors that could enhance the resilience of the port system and quantify the port resilience by applying a Bayesian network [16]. Liu et al. developed an integrated framework using copula-modeling that can help decision-makers understand the effectiveness of resilience performance under various risk conditions [17].

In the above research, after the establishment of the port system resilience evaluation framework, the MCDM methods (e.g., entropy weight method, Fuzzy Analytic Hierarchy Process, CRITIC-entropy method, and TOPSIS method) are widely used to calculate the port comprehensive resilience. However, most of the existing MCDM methods extract the best solution from the decision matrix itself, lacking the consideration of the preferences of decision-makers (i.e., port stakeholders); thus, it is not appropriate to be applied to evaluate the resilience of complex port systems.

2.2. Port Transportation Network Resilience Evaluation

Some scholars regard ports as part of a shipping network or supply chain and use graph theory or complex networks theory to assess the impact of an attack on the resilience of a port or the entire transportation network. Liu et al. proposed a resilience measuring method based on topological indices from graph theory to measure the European port network [3]. Xu et al. developed a modified two-stage container port supply chain system containing a container pretreatment system and a container handling system to enhance its resilience [18]. He et al. proposed a framework to analyze the resilience of the container port shipping network by detecting the changing performance of the network indicators before and after the random attack or one of the deliberate attacks [4]. Chen et al. built an integer programming model to obtain a quantitative measure of the resilience of the port–hinterland container transportation network from the perspective of shippers [19]. Qin et al. proposed the concept of port-node resilience from the perspective of the shipping network and constructed a three-dimensional (structure, function, and location) econometric model of port-node resilience [20]. Gao et al. established a bi-level programming model with two different lower-level models to measure and improve the resilience of port–hinterland container logistics transportation systems [21]. Chen et al. studied the strategic investment of players in a port–hinterland container transportation network to enhance network resilience by adopting network game theory [22]. Li et al. proposed strategies involving capacity sharing and protective cross-port investments through coalition formation to improve the resilience of individual ports in the maritime freight transport system [23]. Verschuur et al. proposed a systemic risk framework for different networks interconnected through ports and described state-of-the-art risk modeling approaches to quantify systemic risks [24].

These studies analyze port resilience considering the prevention before accidents, adaptation during accidents, and recovery after accidents, which have important references for determining the definition of resilience in this study. However, the perspective of these studies is relatively macro, which lacks the consideration of the operational interruption in the port caused by facility or equipment failure. In addition, how to quantitively calculate the impact of facility or equipment failure on port resilience is still unclear, making these studies unsuitable to be used in this study.

3. Methodology

The flowchart of the proposed method is illustrated in Figure 2.

3.1. Three-Level Resilience Evaluation Framework

3.1.1. Influence Factors Analysis

From the perspective of the whole port transportation system, the factors affecting the resilience of specialized terminals can be considered from three levels: micro-level, meso-level, and macro-level.

(1)

Micro-level: inside the specialized terminal

As an important place for ship handling operations in coastal ports, the resilience of specialized terminals is mainly affected by ship, cargo, handling equipment, facilities, and other factors.

Firstly, compared with other ships, ultra-large-scale vessels and dangerous cargo vessels (e.g., crude oil carriers, and Liquefied Natural Gas (LNG) carriers) have higher risks when handling at the terminal, and the losses caused by accidents are also greater. For example, the dangerous cargo explosion accident in the Tianjin Port in August 2015 caused 165 deaths and direct economic losses of CNY 6.866 billion. Therefore, the tonnage of the vessel, the level of dangerous vessel control, and the proportion of dangerous cargo in and out of the terminal should be taken as measurement indicators of resilience, which can be calculated by Appendix A.1, Appendix A.2 and Appendix A.3 in the Appendix A.

Secondly, the failure and damage of terminal facilities and handling equipment will cause the interruption of specialized terminal operations, and the severity of its impact on resilience can be measured by the throughput loss caused by the accident and the repair time after the accident, which can be calculated by Appendix A.4, Appendix A.5, Appendix A.6 and Appendix A.7.

Thirdly, production safety accidents in the terminal will not only cause the interruption of operations but also cause loss of life and personal injury. Concerning the existing industry standards [25], production safety accidents in the terminal can be divided into four levels according to the losses caused: particularly major, major, large, and general, whose influence can be measured by the number of accidents within a period (see Appendix A.8, Appendix A.9, Appendix A.10 and Appendix A.11) and the time to resume normal operations after the accident (see Appendix A.12, Appendix A.13, Appendix A.14 and Appendix A.15).

Finally, berth utilization rate (see Appendix A.16), as an important indicator to measure the busyness of handling operations in specialized terminals, should also be included in the resilience evaluation framework. Specialized terminals with higher berth utilization rates are busier, where accidents have a relatively greater impact on handling operations.

(2)

Meso-level: other port facilities

In addition to specialized terminals, other port facilities such as waterways, collection and distribution systems, port supporting facilities, and management systems will also have an impact on the resilience of specialized terminals.

First of all, the waterway is the inevitable passage for ships to enter and exit coastal ports. The navigation of ships in the waterway is affected by a variety of complex factors such as natural conditions, the number of ships arriving at the port, the scale of the waterway, and navigation rules. With the increase in the number of arrival ships at coastal ports, together with the development of the ship upsizing trend in recent years, the navigation risk of ships in the waterway is gradually increasing. Therefore, the situation of ship accidents in the waterway (i.e., accident grade, number of accidents, and recovery time after accident) should be treated as an important factor to measure the resilience of coastal ports. According to the accident classification of Maritime Traffic Safety Law of the People’s Republic of China [26], this paper classifies water traffic accidents into four levels according to the severity of accidents: particularly major accidents, major accidents, large accidents, and general accidents, whose influence on resilience can be calculated by 8 indicators (see Appendix A.17, Appendix A.18, Appendix A.19, Appendix A.20, Appendix A.21, Appendix A.22, Appendix A.23 and Appendix A.24).

Then, the collection and distribution system is the channel for goods to reach (or leave) the coastal port before and after handling (or unloading) at the specialized terminal. The capacity of the collection and distribution system reflects the scale of goods that a port can receive and displace in a certain period, which is mainly affected by factors such as the grade scale of the channel, the completeness of various collection and distribution modes, etc. When the collection and distribution system is not complete or the capacity is insufficient, the port has a poor ability to cope with emergencies, and it is difficult to achieve cargo evacuation through other modes of transport (e.g., road, railway) in time, affecting the overall operation efficiency of the port. Therefore, the construction of the collection and distribution system (see Appendix A.25) should be used as an indicator to measure specialized resilience.

Next, port supporting facilities, including the port monitoring system, port pipe network and pipeline intelligent monitoring system, port fire safety facilities, port emergency communication and command facilities, port meteorological disaster monitoring system, etc., are important supports for the safe operation of specialized terminals. The more complete the supporting facilities of the port and the higher the degree of information technology, the stronger the monitoring and early warning ability and response ability of the specialized terminal for emergencies. Therefore, port supporting facilities-related indicators (see Appendix A.26, Appendix A.27, Appendix A.28, Appendix A.29 and Appendix A.30) are included in the evaluation framework.

Finally, the advanced management system is important for the safe and efficient operation of the specialized terminal. A complete emergency planning system (see Appendix A.31), emergency drills (see Appendix A.32), and risk assessment methods (see Appendix A.33) are necessary conditions to ensure that coastal ports can respond promptly and recover quickly before, during, and after emergencies.

(3)

Macro-level: corridors and other ports within the transport system

From the macro-level, the port is regarded as a node in the entire transportation system, and the airline is regarded as an edge in the transportation system. When the nodes and edges of the transportation system fail, the efficiency and stability of the entire transportation system will be affected.

Specifically, for the large berths of specialized terminals, when the tonnage is large and the number is small, the fungibility of such berths is poor. Once the berth is unable to operate due to equipment failure or facility damage, other berths that can replace the berth to meet the berthing requirements of large ships in adjacent ports are lacking, which will cause large tonnage ships to be stranded in the port, seriously impacting the overall handling efficiency of the port. What is more, when there are local wars and epidemics, the entire port will be temporarily closed (e.g., the Black Sea port closure caused by the Russia–Ukraine war, the temporary closure of the Yantian port area of Shenzhen port due to COVID-19), making the fungibility of specialized terminals in adjacent ports particularly important. Therefore, according to the tonnage of the berth, this paper considers the number of alternative berths for the largest berths (see Appendix A.34) and the number of alternative berths for representative berths (that is, the berths with the largest number in the port, see Appendix A.35) as evaluation indicators.

Similarly, the stability of the transport system can be seriously affected when the routes of the transport system are blocked due to unexpected events, such as the Suez Canal disruption caused by the Palestinian–Israeli conflict in December 2023. Therefore, the number of alternative transport corridors (see Appendix A.36) should also be included in the evaluation framework.

3.1.2. Construction of Evaluation Framework

Based on the qualitative analysis of the factors affecting the resilience of specialized terminals in the coastal port transportation system in Section 3.1.1, an evaluation framework was constructed, as shown in

Table 1. Evaluation framework for resilience of specialized terminals in coastal ports.

No.	First-Level Indicator	Second-Level Indicator	Third-Level Indicator	Calculation Method	Indicator Type
1	Micro-level (F1)	Terminal (S1)	Ship tonnage (T1)	See Appendix A.1	quantitative
2			Dangerous goods vessel control level (T2)	See Appendix A.2	qualitative
3			Proportion of dangerous goods handled at terminal (T3)	See Appendix A.3	quantitative
4			Rate of change in cargo throughput due to terminal equipment failure (T4)	See Appendix A.4	quantitative
5			Rate of change in cargo throughput due to damage to terminal facilities (T5)	See Appendix A.5	quantitative
6			Mean time to repair equipment failure in terminal (T6)	See Appendix A.6	quantitative
7			Mean time to repair facility damage in terminal (T7)	See Appendix A.7	quantitative
8			Number of particularly major accidents in production safety at terminal (T8)	See Appendix A.8	quantitative
9			Number of major accidents in production safety at terminal (T9)	See Appendix A.9	quantitative
10			Number of large accidents in production safety at terminal (T10)	See Appendix A.10	quantitative
11			Number of general accidents in production safety at terminal (T11)	See Appendix A.11	quantitative
12			Recovery time of particularly major accidents in production safety at terminal (T12)	See Appendix A.12	quantitative
13			Recovery time of major accidents in production safety at terminal (T13)	See Appendix A.13	quantitative
14			Recovery time of large accidents in production safety at terminal (T14)	See Appendix A.14	quantitative
15			Recovery time of general accidents in production safety at terminal (T15)	See Appendix A.15	quantitative
16			Average berth utilization rate of terminal (T16)	See Appendix A.16	quantitative
17	Meso-level (F2)	Waterway (S2)	Number of particularly major water traffic accidents (T17)	See Appendix A.17	quantitative
18			Number of major water traffic accidents (T18)	See Appendix A.18	quantitative
19			Number of large water traffic accidents (T19)	See Appendix A.19	quantitative
20			Number of general water traffic accidents (T20)	See Appendix A.20	quantitative
21			Recovery time of particularly major water traffic accidents (T21)	See Appendix A.21	quantitative
22			Recovery time of major water traffic accidents (T22)	See Appendix A.22	quantitative
23			Recovery time of large water traffic accidents (T23)	See Appendix A.23	quantitative
24			Recovery time of general water traffic accidents (T24)	See Appendix A.24	quantitative
25		Collecting and distributing system (S3)	Construction of collection and distribution system (T25)	See Appendix A.25	qualitative
26		Port supporting facilities (S4)	Port monitoring coverage (T26)	See Appendix A.26	quantitative
27			Intelligent monitoring and management rate of port pipe network pipeline (T27)	See Appendix A.27	quantitative
28			Construction of port fire safety facilities (T28)	See Appendix A.28	qualitative
29			Construction of port emergency communication command facilities (T29)	See Appendix A.29	qualitative
30			Construction of port meteorological disaster monitoring system (T30)	See Appendix A.30	qualitative
31		Management system (S5)	Emergency plan system (T31)	See Appendix A.31	qualitative
32			Emergency drill carried out (T32)	See Appendix A.32	qualitative
33			Port integrated risk assessment (T33)	See Appendix A.33	qualitative
34	Marco-level (F3)	Port transportation system (S6)	The number of alternative berths for largest berths (T34)	See Appendix A.34	quantitative
35			The number of alternative berths for representative berths (T35)	See Appendix A.35	quantitative
36			The number of alternative transport channels (T36)	See Appendix A.36	quantitative

. The first level of the resilience framework considers the micro-level, meso-level, and macro-level. The second-level indicators are specifically divided into the terminal, waterway, collection and distribution system, port supporting facilities, management system, and port transportation system. The third-level indicators include a total of 36 qualitative and quantitative indicators.

The description and calculation methods of each third-level indicator are proposed in Appendix A. It is noticeable that quantitative indicators are calculated according to the calculation method or formula given in Appendix A directly, while qualitative indicators are divided by experts based on their various indicators into 7 grades: Very Poor (VP), Poor (P), Medium Poor (MP), Fair (F), Medium Good (MG), Good (G), Very Good (VG).

3.2. Improved RBOP Model

3.2.1. Optimum Alternative, Optimal Alternative, and the Improvement of RBOP

The RBOP method was first proposed by Zakeri et al. in 2019 [27], whose core idea was to simulate the behavior pattern of decision-makers for MCDM. Different from other MCDM methods to extract the best scheme from the decision matrix itself, RBOP defines two sets of alternative schemes derived from the decision problem according to the decision-maker, which are called optimum alternative and optimal alternative, and considers that the best scheme is located in the position closest to the optimum alternative and the optimal alternative at the same time.

(1)

Optimum alternative

Optimum alternative is an abstract alternative generated by the decision-maker according to the initial decision matrix; the number of the best alternative is greater than or equal to the number of the original problem, whose purpose is to facilitate the decision-maker to evaluate the initial decision matrix according to some specific reservation criteria in the decision process. Compared with the initial decision matrix, the best alternative should meet the following conditions:

Let $S_i$ represent the overall score of the ith alternative, ${S^{\prime }}_i$ refers to the overall score of the optimum alternative, and $D_i$ is the distance between the optimum alternative and the overall score of the ith alternative. Then, the best alternative should satisfy Equations (1)–(3) at the same time.

$${S^{\prime }}_i<2S_i$$

(1)

$${\displaystyle \frac{{S^{\prime }}_i}{S_i}}>1$$

(2)

$$D_i<S_i$$

(3)

(2)

Optimal alternative

The optimal alternative can satisfy the decision-maker’s requirement for all alternatives, that is, the value of the optimal alternative is greater than any initial alternative under each decision criterion. For the problem of coastal port system resilience assessment, the best alternative is usually an abstract alternative port, which does not exist in the actual situation.

(3)

The improvement of RBOP

Since the selection of the optimum alternative has an important impact on the evaluation results of the RBOP algorithm, in this study, the optimum alternative is determined through experts’ evaluation. The experts will evaluate the field investigation and future development trend of the target port to determine the proper optimum alternative, meeting the requirements of the original RBOP method.

Details of the experts invited to participate in the evaluation of this study are shown in

Table 2. Details of the experts invited for this study.

No.	Institute	Education	Experience (Year)
1	Dalian University of Technology	Ph.D.	Professor (28)
2	Dalian Maritime University	Ph.D.	Professor (30)
3	Wuhan University of Technology	Ph.D.	Professor (20)
4	Shanghai Maritime University	Ph.D.	Professor (7)
5	Ningbo China Communications Water Transportation Design and Research Co., LTD	Master’s	Manager (10)
6	Zhoushan Pilot Station	Master’s	Director (19)
7	Ningbo Maritime Safety Administration	Master’s	Director (13)
8	Ningbo Port and Shipping Management Center	Master’s	Manager (16)
9	Transport Planning and Research Institute Ministry of Transport	Master’s	Manager (15)
10	Shandong Port Group Co., LTD	Master’s	Manager (10)

, including professors in universities, managers in port design institutes, masters in pilot stations and maritime safety administrations, as well as masters in port enterprises.

3.2.2. Calculation Procedure

The calculation process of RBOP is as follows:

Step 1: Construct the initial decision matrix $\mathit{X}=\left[x_{ij}\right],i=\left\{1,2,\dots ,m\right\},j=\left\{1,2,\dots ,n\right\}$, where $x_{ij}$ is the jth evaluation criterion value of the ith alternative port in the initial decision matrix.

Step 2: According to the initial decision matrix, construct the optimum alternative matrix by expert evaluation method ${\mathit{X}}^{\prime }$=$\left[{x^{\prime }}_{ij}\right],i=\left\{1,2,\dots ,m\right\},j=\{1,2,\dots ,n\}$, where ${x^{\prime }}_{ij}$ is the jth evaluation criterion value of the ith alternative port in the optimum alternative matrix. Each of the optimum alternatives of ${\mathit{X}}^{\prime }$ shall simultaneously satisfy Equations (1)–(3).

Step 3: Determine the normalized matrix of the initial decision matrix $\mathit{N}$ and the normalized matrix of the optimum alternative matrix ${\mathit{N}}^{\prime }$ by Equations (4)–(9):

$$\mathit{N}=\left\{\begin{array}{c}\left[N_{ij}^{+}\right] \mathrm{i}\mathrm{f} j \mathrm{i}\mathrm{s} \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\\ \left[N_{ij}^{-}\right] \mathrm{i}\mathrm{f} j \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\end{array}\right.$$

(4)

$${\mathit{N}}^{\prime }=\left\{\begin{array}{c}\left[{N^{\prime }}_{ij}^{+}\right] \mathrm{i}\mathrm{f} j \mathrm{i}\mathrm{s} \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\\ \left[{N^{\prime }}_{ij}^{-}\right] \mathrm{i}\mathrm{f} j \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\end{array}\right.$$

(5)

$$N_{ij}^{+}=x_{ij}\times {\left(\underset{1\le i\le m}{\max }\left\{x_{ij}\right\}\right)}^{-1}$$

(6)

$$N_{ij}^{-}=\underset{1\le i\le m}{\min }\left\{x_{ij}\right\}\times {\left(x_{ij}\right)}^{-1}$$

(7)

$${N^{\prime }}_{ij}^{+}={x^{\prime }}_{ij}\times {\left(\underset{1\le i\le m}{\max }\left\{{x^{\prime }}_{ij}\right\}\right)}^{-1}$$

(8)

$${N^{\prime }}_{ij}^{-}=\underset{1\le i\le m}{\min }\left\{{x^{\prime }}_{ij}\right\}\times {\left({x^{\prime }}_{ij}\right)}^{-1}$$

(9)

where the larger the value of the benefit criteria, the better the evaluation result, while the cost criteria are the opposite.

Step 4: Build the weighted normalized matrix for initial decision matrix and optimum alternative matrix, denoted as $\mathit{R}$ and ${\mathit{R}}^{\prime }$:

$$\mathit{R}=\left[r_{ij}\right]=w_j\times \mathit{N},i=\left\{1,2,\dots ,m\right\},j=\left\{1,2,\dots ,n\right\}$$

(10)

$${\mathit{R}}^{\prime }=\left[{r^{\prime }}_{ij}\right]=w_j\times {\mathit{N}}^{\prime },i=\left\{1,2,\dots ,m\right\},j=\{1,2,\dots ,n\}$$

(11)

where $w_j$ refers to the weight of indicator j, which is determined by experts’ evaluation and meet ${\sum _{1\le j\le n}w}_j=1$.

Step 5: Construct the optimum point matrix $\mathit{\alpha }=\left[{\alpha }_{ij}\right],i=\left\{1,2,\dots ,m\right\},j=\{1,2,\dots ,n\}$.

$${\alpha }_{ij}={\left(r_{ij}^2+{r^{\prime }}_{ij}^2\right)}^{1/2}$$

(12)

Step 6: Define the optimal alternative matrix $\mathsf{\Theta }=\left[{\Theta }_j\right],j=\left\{1,2,\dots ,n\right\}.$

Step 7: Calculate the normalized matrix of the optimal alternative matrix ${\mathsf{\Theta }}_{\mathit{N}}=\left[{\Theta }_{N_j}\right],j=\left\{1,2,\dots ,n\right\}.$

$${\Theta }_{N_j}=\left\{\begin{array}{c}{\Theta }_j\times {\left(\underset{1\le i\le m}{\max }\{x_{ij},{\Theta }_j\}\right)}^{-1} \mathrm{i}\mathrm{f} j \mathrm{i}\mathrm{s} \mathrm{b}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\\ \underset{1\le i\le m}{\min }\{x_{ij},{\Theta }_j\}\times {\left({\Theta }_j\right)}^{-1} \mathrm{i}\mathrm{f} j \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a}\end{array}\right.$$

(13)

Step 8: Construct the weighted normalized matrix of the optimal alternative matrix ${{\mathsf{\Theta }}^{\prime }}_{\mathit{N}}=\left[{{\Theta }^{\prime }}_{N_j}\right],j=\left\{1,2,\dots ,n\right\}.$

$${{\Theta }^{\prime }}_{N_j}=w_j\times {\Theta }_{N_j}$$

(14)

Step 9: Determine optimal point matrix $\mathsf{\Phi }=\left[{\Phi }_{ij}\right]$, and order the resilience of alternative ports according to the value of ${\mathcal{R}}_i=\sum _{i=1}^m{\Phi }_{ij}$. The larger the ${\mathcal{R}}_i$, the better the port i’s resilience.

$${\Phi }_{ij}={\displaystyle \frac{{{\Theta }^{\prime }}_{N_j}+{\alpha }_{ij}}{2}}$$

(15)

4. Application and Results

4.1. Object-Specialized Terminal Selection

Considering the development and layout status of coastal container ports, this paper selects the specialized container terminal in eight trunk ports in coastal China as the objective, including Dalian Port, Tianjin Port, Qingdao Port, Shanghai Port, Ningbo Zhoushan Port, Xiamen Port, Shenzhen Port, and Guangzhou Port, to verify the effectiveness of the proposed method.

According to the evaluation framework of the specialized terminal, considering the data availability, this paper selects nine indicators, including the rate of change in cargo throughput due to terminal equipment failure (T₄), mean time to repair equipment failure in the terminal (T₆), average berth utilization rate of the terminal (T₁₆), number of general water traffic accidents (T₂₀), recovery time of large water traffic accidents (T₂₃), recovery time of general water traffic accidents (T₂₄), construction of collection and distribution system (T₂₅), number of alternative berths for largest berths (T₃₄), and number of alternative berths for representative berths (T₃₅), to evaluate the resilience of the object-specialized terminal.

4.2. Results Analysis

(1)

Step 1

According to the calculation method in Appendix A, the values of nine resilience evaluation indicators of eight object ports are determined, whose results are shown in

Table 3. Value of nine resilience evaluation indicators of eight object ports.

xij	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	4.76%	23.07	46%	12	70	38	F	1	8
Guangzhou Port	1.42%	22.33	57%	12	89	21	VG	25	59
Ningbo Zhoushan Port	1.60%	24.71	72%	19	195	68	G	1	32
Qingdao Port	2.62%	23.62	65%	14	140	60	F	13	13
Xiamen Port	2.36%	23.06	50%	7	144	62	MP	10	10
Shanghai Port	1.08%	23.53	81%	14	80	68	G	25	42
Shenzhen Port	1.31%	24.04	78%	18	130	74	VG	1	59
Tianjin Port	1.98%	24.11	53%	13	144	4	MG	2	22

.

In Table 3, since T₂₅ is a linguistic variable, it can be translated to a numerical variable according to

Table 4. Relationship between linguistic variable and numerical variable.

Linguistic Variable	Numerical Variable
Very Poor (VP)	1
Poor (P)	2
Medium Poor (MP)	3
Fair (F)	4
Medium Good (MG)	5
Good (G)	6
Very Good (VG)	7

. In addition, the percentages of T₄ and T₁₆ can be converted to decimals. In this way, the initial decision matrix $\mathit{X}$ can be determined, as shown in

Table 5. Initial decision matrix $\mathit{X}$.

${\mathit{x}}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.0476	23.07	0.46	12.00	70.00	38.00	4.00	1.00	8.00
Guangzhou Port	0.0142	22.33	0.57	12.00	89.00	21.00	7.00	25.00	59.00
Ningbo Zhoushan Port	0.0160	24.71	0.72	19.00	195.00	68.00	6.00	1.00	32.00
Qingdao Port	0.0262	23.62	0.65	14.00	140.00	60.00	4.00	13.00	13.00
Xiamen Port	0.0236	23.06	0.50	7.00	144.00	62.00	3.00	10.00	10.00
Shanghai Port	0.0108	23.53	0.81	14.00	80.00	68.00	6.00	25.00	42.00
Shenzhen Port	0.0131	24.04	0.78	18.00	130.00	74.00	7.00	1.00	59.00
Tianjin Port	0.0198	24.11	0.53	13.00	144.00	4.00	5.00	2.00	22.00

.

(2)

Step 2

According to Table 5, considering the future development trend of the object port, 10 experts in port engineering are invited to determine the optimum alternative matrix, as shown in

Table 6. Optimum alternative matrix ${\mathit{X}}^{\prime }$.

${{\mathit{x}}^{\prime }}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.0300	22.00	0.40	8.00	50.00	30.00	5.00	2.00	10.00
Guangzhou Port	0.0100	21.00	0.50	8.00	65.00	15.00	7.00	25.00	60.00
Ningbo Zhoushan Port	0.0100	23.00	0.65	12.00	120.00	50.00	7.00	2.00	35.00
Qingdao Port	0.0200	23.00	0.60	10.00	100.00	45.00	5.00	15.00	15.00
Xiamen Port	0.0200	22.00	0.45	5.00	100.00	45.00	4.00	13.00	13.00
Shanghai Port	0.0100	23.00	0.70	10.00	60.00	50.00	7.00	25.00	45.00
Shenzhen Port	0.0100	23.00	0.70	12.00	90.00	55.00	7.00	2.00	60.00
Tianjin Port	0.0100	23.00	0.45	10.00	100.00	3.00	6.00	3.00	25.00

.

(3)

Step 3

The normalized matrix of the initial decision matrix $\mathit{N}$ and the normalized matrix of the optimum alternative matrix ${\mathit{N}}^{\prime }$ can then be calculated, which are shown in

Table 7. Normalized matrix of initial decision matrix $\mathit{N}$.

${\mathit{N}}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.2269	0.9679	1.0000	0.5833	1.0000	0.1053	0.5714	0.0400	0.1356
Guangzhou Port	0.7606	1.0000	0.8070	0.5833	0.7865	0.1905	1.0000	1.0000	1.0000
Ningbo Zhoushan Port	0.6750	0.9037	0.6389	0.3684	0.3590	0.0588	0.8571	0.0400	0.5424
Qingdao Port	0.4122	0.9454	0.7077	0.5000	0.5000	0.0667	0.5714	0.5200	0.2203
Xiamen Port	0.4576	0.9683	0.9200	1.0000	0.4861	0.0645	0.4268	0.4000	0.1695
Shanghai Port	1.0000	0.9490	0.5679	0.5000	0.8750	0.0588	0.8571	1.0000	0.7119
Shenzhen Port	0.8244	0.9289	0.5897	0.3889	0.5385	0.0541	1.0000	0.0400	1.0000
Tianjin Port	0.5455	0.9262	0.8679	0.5385	0.4861	1.0000	0.7143	0.0800	0.3729

and

Table 8. Normalized matrix of the optimum alternative matrix ${\mathit{N}}^{\prime }$.

${{\mathit{N}}^{\prime }}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.3333	0.9545	1.0000	0.6250	1.0000	0.1000	0.7143	0.0800	0.1667
Guangzhou Port	1.0000	1.0000	0.8000	0.6250	0.7692	0.2000	1.0000	1.0000	1.0000
Ningbo Zhoushan Port	1.0000	0.9130	0.6154	0.4167	0.4167	0.0600	1.0000	0.0800	0.5833
Qingdao Port	0.5000	0.9130	0.6667	0.5000	0.5000	0.0667	0.7143	0.6000	0.2500
Xiamen Port	0.5000	0.9545	0.8889	1.0000	0.5000	0.0667	0.5714	0.5200	0.2167
Shanghai Port	1.0000	0.9130	0.5714	0.5000	0.8333	0.0600	1.0000	1.0000	0.7500
Shenzhen Port	1.0000	0.9130	0.5714	0.4167	0.5556	0.0545	1.0000	0.0800	1.0000
Tianjin Port	1.0000	0.9130	0.8889	0.5000	0.5000	1.0000	0.8571	0.1200	0.4167

, respectively.

(4)

Step 4

Based on Table 7 and Table 8, the weighted normalized matrix for the initial decision matrix and optimum alternative matrix, $\mathit{R}$ and ${\mathit{R}}^{\prime }$, can be obtained (See

Table 9. Weighted normalized matrix for initial decision matrix $\mathit{R}$.

${\mathit{r}}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.0324	0.1383	0.1429	0.0833	0.0714	0.0075	0.0816	0.0029	0.0097
Guangzhou Port	0.1087	0.1429	0.1153	0.0833	0.0562	0.0136	0.1429	0.0714	0.0714
Ningbo Zhoushan Port	0.0964	0.1291	0.0913	0.0526	0.0256	0.0042	0.1224	0.0029	0.0387
Qingdao Port	0.0589	0.1351	0.1011	0.0714	0.0357	0.0048	0.0816	0.0371	0.0157
Xiamen Port	0.0654	0.1383	0.1314	0.1429	0.0347	0.0046	0.0612	0.0286	0.0121
Shanghai Port	0.1429	0.1356	0.0811	0.0714	0.0625	0.0042	0.1224	0.0714	0.0508
Shenzhen Port	0.1178	0.1327	0.0842	0.0556	0.0385	0.0039	0.1429	0.0029	0.0714
Tianjin Port	0.0779	0.1323	0.1240	0.0769	0.0347	0.0714	0.1020	0.0057	0.0266

and

Table 10. Weighted normalized matrix for optimum decision matrix ${\mathit{R}}^{\prime }$.

${{\mathit{r}}^{\prime }}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.0476	0.1364	0.1429	0.0893	0.0714	0.0071	0.1020	0.0057	0.0119
Guangzhou Port	0.1429	0.1429	0.1143	0.0893	0.0549	0.0143	0.1429	0.0714	0.0714
Ningbo Zhoushan Port	0.1429	0.1304	0.0879	0.0595	0.0298	0.0043	0.1429	0.0057	0.0417
Qingdao Port	0.0714	0.1304	0.0952	0.0714	0.0357	0.0048	0.1020	0.0429	0.0179
Xiamen Port	0.0714	0.1364	0.1270	0.1429	0.0357	0.0048	0.0816	0.0371	0.0155
Shanghai Port	0.1429	0.1304	0.0816	0.0714	0.0595	0.0043	0.1429	0.0714	0.0536
Shenzhen Port	0.1429	0.1304	0.0816	0.0595	0.0397	0.0039	0.1429	0.0057	0.0714
Tianjin Port	0.1429	0.1304	0.1270	0.0714	0.0357	0.0714	0.1224	0.0086	0.0298

). The weight of each evaluation criterion, $w_j=\{0.143,0.143,0.143,0.143,0.071,0.071,0.143,0.071,0.071\}$, is determined by expert assessment, where the weights of T₂₃, T₂₄, T₃₄, and T₃₅ are half of other criterions, since T₂₃ and T₂₄ are the recovery times of different grade water traffic accidents, while both T₃₄ and T₃₅ focus on the number of alternative berths.

(5)

Step 5

The optimum point matrix $\mathit{\alpha }$ can be determined, as shown in

Table 11. Optimum point matrix $\mathit{\alpha }$.

${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.0576	0.1942	0.2020	0.1221	0.1010	0.0104	0.1307	0.0064	0.0153
Guangzhou Port	0.1795	0.2020	0.1623	0.1221	0.0786	0.0197	0.2020	0.1010	0.1010
Ningbo Zhoushan Port	0.1724	0.1835	0.1267	0.0795	0.0393	0.0060	0.1882	0.0064	0.0569
Qingdao Port	0.0926	0.1878	0.1389	0.1010	0.0505	0.0067	0.1307	0.0567	0.0238
Xiamen Port	0.0968	0.1942	0.1828	0.2020	0.0498	0.0066	0.1020	0.0469	0.0196
Shanghai Port	0.2020	0.1881	0.1151	0.1010	0.0863	0.0060	0.1882	0.1010	0.0739
Shenzhen Port	0.1851	0.1861	0.1173	0.0814	0.0553	0.0055	0.2020	0.0064	0.1010
Tianjin Port	0.1627	0.1858	0.1775	0.1050	0.0498	0.1010	0.1594	0.0103	0.0399

.

(6)

Step 6

According to expert evaluation, the optimal alternative matrix $\mathsf{\Theta }=\{0.01,20,0.4,3,30,2,10,30,65\}$ can be determined, which is an abstract alternative with the most ideal situation.

(7)

Step 7

The normalized matrix of the optimal alternative matrix can be calculated, ${\mathsf{\Theta }}_{\mathit{N}}=\{1,1.05,1,1.667,1.667,1.5,\mathrm{1,1.2},1.083\}$, which shows that, except for T₄, T₁₆, and T₂₅, other indicators of the optimal alternative are better than the ones of the optimum alternative.

(8)

Step 8

The weighted normalized matrix of the optimal alternative matrix can be constructed, ${{\mathsf{\Theta }}^{\prime }}_{\mathit{N}}=\{0.143,0.150,0.143,0.238,0.119,0.107,0.143,0.086,0.077,\}$, whose weight also adopts $w_j$.

(9)

Step 9

Finally, the optimal point matrix $\mathsf{\Phi }$ and corresponding ${\mathcal{R}}_i$ can be obtained, as shown in

Table 12. Optimal point matrix $\mathsf{\Phi }$ and ${\mathcal{R}}_i.$.

${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+	${\mathcal{R}}_{\mathit{i}}$	Rank
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.100	0.172	0.172	0.180	0.110	0.059	0.137	0.046	0.046	1.023	7
Guangzhou Port	0.161	0.176	0.153	0.180	0.099	0.063	0.172	0.093	0.089	1.187	1
Ningbo Zhoushan Port	0.158	0.167	0.135	0.159	0.079	0.057	0.166	0.046	0.067	1.032	6
Qingdao Port	0.118	0.169	0.141	0.170	0.085	0.057	0.137	0.071	0.051	0.997	8
Xiamen Port	0.120	0.172	0.163	0.220	0.084	0.057	0.122	0.066	0.049	1.053	5
Shanghai Port	0.172	0.169	0.129	0.170	0.103	0.057	0.166	0.093	0.076	1.134	2
Shenzhen Port	0.164	0.168	0.130	0.160	0.087	0.056	0.172	0.046	0.089	1.073	4
Tianjin Port	0.153	0.168	0.160	0.172	0.084	0.104	0.151	0.048	0.059	1.099	3

.

From Table 12, it can be seen that the resilience ranking of specialized container terminals from highest to lowest is Guangzhou Port, Shanghai Port, Tianjin Port, Shenzhen Port, Xiamen Port, Ningbo Zhoushan Port, Dalian Port, and Qingdao Port.

For further analysis, the ${\alpha }_{ij}$ value of each evaluation criterion for each port is presented in Figure 3. It is clear that the ${\alpha }_{ij}$ value of each evaluation criterion for the port with better resilience is basically higher than the one with lower resilience. For example, the ${\alpha }_{ij}$ value ranks for Guangzhou Port (ranked first in overall resilience) of each evaluation criterion are 3, 1, 4, 2, 3, 7, 1, 1, and 1, while the ones for Shanghai (ranked second in overall resilience) are 1, 4, 8, 5, 2, 3, 3, 1, and 3. The ${\alpha }_{ij}$ values of T₂₃, T₂₄, T₃₄, and T₃₅ are around half of the other evaluation criterions, which reflects the lower weights of T₂₃, T₂₄, T₃₄, and T₃₅ compared with other evaluation criterions. In addition, the bottleneck of the resilience for certain specialized terminals can also be analyzed. Taking Dalian Port as an example, its low overall resilience is mainly caused by its high equipment failure rate (T₄), relatively backward collection and distribution system (T₂₅), and poor berth fungibility (T₃₄, T₃₅).

4.3. Comparison

4.3.1. Comparison of the Improved RBOP with Existing MCDM Methods

The results of the improved RBOP method are compared with the existing MCDM methods, including TOPSIS [28], VIKOR [29], Multi-MOORA [30], and WASPAS [31], and the comparison results are shown in

Table 13. Results comparison of improved RBOP and other MCDM methods.

Port	RBOP		TOPSIS		VIKOR		Multi-MOORA		WASPAS
	${\mathcal{R}}_{\mathit{i}}$	Rank	${\mathit{R}}_{\mathit{i}}$	Rank	$\mathit{Q}$	Rank	${\mathit{s}\mathit{r}}_{\mathit{i}}$	Rank	${\mathit{W}}_{\mathit{i}}$	Rank
Dalian Port	1.023	7	0.323	8	0.857	7	24	8	0.478	8
Guangzhou Port	1.187	1	0.829	1	0	1	3	1	0.78	1
Ningbo Zhoushan Port	1.032	6	0.502	5	1	8	19	7	0.5	6
Qingdao Port	0.997	8	0.441	7	0.679	3	13	4	0.495	7
Xiamen Port	1.053	5	0.493	6	0.802	5	17	6	0.539	5
Shanghai Port	1.134	2	0.677	2	0.751	4	6	2	0.697	2
Shenzhen Port	1.073	4	0.562	3	0.808	6	16	5	0.566	4
Tianjin Port	1.099	3	0.559	4	0.584	2	10	3	0.611	3

. Note that the criteria weight of each method is the same as that of RBOP, and the value of v in VIKOR and the one of λ in WASPAS are both set as 0.5.

To present the port ranking results under different MCDA methods more clearly, the data has been visualized in Figure 4. It can be seen that there are some differences between the results of the improved RBOP and the results of the existing MCDM method, where the ranking results of the improved RBOP and WASPAS are the closest and only differ in the seventh and eighth ranking. In addition, compared with other MCDM methods, since the improved RBOP method invites industry experts to determine the optimum alternative for the object port by judging their current situation and future development trend, the improved RBOP method considers more information beyond the initial decision matrix, making its results more in line with the expectations of decision-makers (industry experts).

4.3.2. Influences of Experts’ Evaluation on Optimum Alternative for Each Object Port

To analyze the impact of expert evaluations on the optimum alternative for each port, we have provided another case (denoted as case 1). In this case, the experts unanimously agree that the future development trends of each target port are the same. This is reflected in the RBOP method as the optimum alternative being the same for every port (i.e., RBOP without experts’ evaluation on optimum alternative). In case 1, we uniformly set it to the level achieved by the port with the best performance in a certain indicator (as shown in

Table 14. Optimum alternative matrix ${\mathit{X}}^{\prime }$ in case 1.

${{\mathit{x}}^{\prime }}_{\mathit{i}\mathit{j}}$	−	−	−	−	−	−	+	+	+
	T4	T6	T16	T20	T23	T24	T25	T34	T35
Dalian Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Guangzhou Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Ningbo Zhoushan Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Qingdao Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Xiamen Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Shanghai Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Shenzhen Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00
Tianjin Port	0.0100	21.00	25.00	60.00	0.40	5.00	50.00	3.00	7.00

).

In case 1, we calculated the ${\mathcal{R}}_{\mathit{i}}$ value and ranking of each port step by step using the RBOP method. The results are compared with those of the improved RBOP method proposed in this paper, as shown in

Table 15. Comparison of RBOP with and without experts’ evaluation on optimum alternative.

Port	Improved RBOP Method		RBOP Without Experts’ Evaluation on Optimum Alternative
	${\mathcal{R}}_{\mathit{i}}$	Rank	${\mathcal{R}}_{\mathit{i}}$	Rank
Dalian Port	1.023	7	1.200	6
Guangzhou Port	1.187	1	1.252	1
Ningbo Zhoushan Port	1.032	6	1.190	7
Qingdao Port	0.997	8	1.181	8
Xiamen Port	1.053	5	1.207	5
Shanghai Port	1.134	2	1.236	2
Shenzhen Port	1.073	4	1.216	3
Tianjin Port	1.099	3	1.209	4

. It can be seen from the table that the top two ports remain unchanged, still being Guangzhou Port and Shanghai Port. However, the rankings of Tianjin Port and Shenzhen Port, originally third and fourth, are swapped. Similarly, the rankings of Ningbo Zhoushan Port and Dalian Port, originally sixth and seventh, are also swapped.

In addition, when comparing the results of case 1 with those of other MCDM methods in Table 13, it can be observed that they are most similar to the TOPSIS results. This is easily understandable because, without incorporating expert evaluations to improve the RBOP method, the final ranking of RBOP, like TOPSIS, is solely based on the initial input itself and is independent of the more subjective expert evaluations. This comparison result further demonstrates the necessity of introducing expert evaluations to improve the RBOP method in this study.

4.4. Discussion

In this paper, we introduce experts’ evaluations to improve the RBOP method for better assessment of specialized terminal resilience. The experts’ evaluations are used in the following three aspects.

(1)

For qualitative indicators in the resilience evaluation framework, the experts will evaluate their condition into seven grades (i.e., from Very Good to Very Poor). For example, for indicator T₂₅ (i.e., construction of collection and distribution system), the experts will consider whether there is an inland waterway, whether the port has an inbound railway, and the number of lanes on the inbound highway in specialized terminals. If the specialized terminals have neither an inland waterway nor inbound highway, its T₂₅ value will be Very Poor.

(2)

The optimum alternative for each object port, which reflects the possible best condition of the object port, is also determined by experts’ evaluation. Different experts may have significant differences in their judgments on the future development trend of the same port, which is the reason why we need to consider various experts’ ideas to determine the optimum alternative matrix.

(3)

The weight of each evaluation criterion $w_j$ is obtained according to experts’ evaluation. The experts will consider the possible relationship between items in the same second-level indicator such as the number of alternative berths for largest berths (T₃₄) and representative berths (T₃₅). The weight of each evaluation criterion $w_j$ can be very important when we consider many criterions to calculate port resilience.

From the comparison results of the improved RBOP method and other MCDM methods (i.e., TOPSIS, VIKOR, Multi-MOORA, and WASPAS), it can be seen that the improved RBOP method is better than the latest method (i.e., WASPAS). The improved RBOP method results align more closely with expert expectations due to the introduction of experts’ evaluations. The method proposed in this paper has the ability to be extended to any specialized port in the world for the purpose of evaluating its comprehensive resilience from the micro-level, meso-level, and macro-level. However, since the calculation methods for some of the indicators proposed in this study were inspired by existing port operation standards in China (e.g., T₈, T₁₇, etc.), when applying the proposed method to foreign ports, these indicator calculation methods should be re-evaluated in accordance with local port standards.

The main shortcoming of this study lies in the case analysis. Due to the difficulty of data acquisition, the data of nine indicators (three micro-level indicators, four meso-level indicators, and two macro-level indicators) can be obtained from port operators; thus, these nine representative indicators are selected from thirty-six evaluation indicators for analysis. In the future, when the proposed method is applied to the specialized terminal assessment of actual ports, more comprehensive data can be collected to obtain more accurate results for assessing the specialized terminal resilience of coastal ports.

5. Conclusions

With the rapid development of the shipping industry, specialized terminals play an increasingly important role in the coastal port transportation system and even the whole shipping network. The good resilience of specialized terminals is the basis for efficiency of the coastal port transportation system and the stability of shipping networks. To evaluate the resilience of specialized terminals and identify bottlenecks of the coastal port transportation system, the factors affecting the specialized terminals’ resilience from the perspective of the overall coastal port transportation system at the micro-level, meso-level, and macro-level are first qualitatively analyzed in this study. Then, the resilience evaluation framework of the specialized terminal is constructed, and the quantitative calculation method of each evaluation indicator is proposed. After that, an improved RBOP method is proposed to evaluate the comprehensive resilience of specialized terminals. Finally, the specialized container terminal in eight trunk ports in coastal China is employed as the case study to verify the effectiveness of the proposed method, whose results are also compared with existing MCDM methods. Some beneficial conclusions are obtained from this study:

(1)

Since the improved RBOP method introduces expert evaluation when determining the optimum and optimal alternatives, compared with other MCDM methods, the proposed method takes into account the current status and future development trend of the specialized terminals in the object port. Therefore, the resilience assessment result shows some differences from the existing MCDM methods, which are more in line with experts’ expectations.

(2)

In the case study, the resilience ranking of specialized container terminals from highest to lowest is Guangzhou Port, Shanghai Port, Tianjin Port, Shenzhen Port, Xiamen Port, Ningbo Zhoushan Port, Dalian Port, and Qingdao Port. The bottleneck of the specialized terminals’ resilience in each object port can also be analyzed from the optimal point matrix. For example, the main factors leading to the poor resilience of specialized container terminals in Dalian Port are the high equipment failure rate, relatively backward collection and distribution system, and poor berth fungibility.